Two people once testified that they saw the moon in the east at morning and in the west at night.

R. Yochanan ben Nuri rejected their testimony, but Raban Gamliel accepted it.

Two people once testified that they saw the moon on the day of the 30th, but it was not seen the following evening.

Raban Gamliel accepted their testimony.

(R. Dosa ben Hurkenos): "They are false; it is like a woman giving birth later being seen pregnant!"

(R. Yehoshua): Agreed.

Raban Gamliel ordered R. Yehoshua to come to him with his stick and money on the 11th of Tishrei (which he would consider to be Yom Kipur).

R. Akiva comforted him by telling him that Rosh Chodesh is whenever Beis Din say it is, correct or not.

R. Dosa ben Hurkenos pointed out that analyzing the accuracy of Raban Gamliel's judgments would also require analyzing the accuracy of all previous Batei Din.

The seventy elders in Moshe's Beis Din are not named so that the Beis Din of any generation can be argued to be as great.

When R. Yehoshua went to Raban Gamliel, he kissed him, calling him his master in wisdom, and his student in obedience.

(Raban Gamliel): Sometimes the moon's orbit is long, sometimes short.

The source is a Pasuk which states that the sun has a regular path, but (by implication) not the moon.

R. Chiya saw the old moon on the morning of the 29th of Elul;

He threw a clod of earth at it, as he wanted it to be invisible now so that the new one could appear at night (and the month could be abridged, thereby separating Yom Kipur from Shabbos).

Rebbi told him to go to Ein Tav and sanctify Rosh Chodesh there, and to send the message "David Melech Yisrael..."

(Beraisa): Once, it looked like a new moon had appeared on the 29th, and they wanted to declare Rosh Chodesh.

Raban Gamliel told them that a month cannot be shorter than 29 1/2 days, 40 minutes and 73 Chalakim.

He gave an extensive Hesped on that day to publicize that it was not Rosh Chodesh.

Question: Was R. Yehoshua in distress, or R. Akiva?

Answer: R. Yehoshua was in distress, wishing to fall sick for a year rather than have to travel on what he considered to be Yom Kipur.

R. Akiva, with his permission, pointed out that the Pasuk says "You" three times to teach that Beis Din's decisions on the calendar stand even if they are mistaken, deliberately inaccurate, or based on false testimony.

R. Yehoshua told him that he had comforted him.

(Beraisa): The names of the seventy elders are not mentioned so as to prevent people from saying, "Are our judges like Moshe and all the rest?!"

Likewise, the Pasuk states that Hash-m sent Yeruba'al, Badan and Yiftach;

Gidon was called Yeruba'al because he fought against Ba'al.

Shimshon was called Badan because he was descended from Dan.

Another Pasuk equates Shmuel with Moshe and Aharon.

In combination, the Pesukim equates the first three (lesser) people with the last three (greater) people, teaching us that each was just as great for his generation.

This teaches us that even the least of people who is appointed over the community is as the greatest.

Likewise, the Pasuk instructs a person to go to the judge "of his day"; obviously there's no other judge to got to, but it teaches us that none other should be wanted.

Likewise, the Pasuk tells us not to say that earlier generations were superior.

When Raban Gamliel saw R. Yehoshua, he stood up and kissed him.

He said, "Welcome, my teacher (of Torah in public) and my disciple (who accepts my orders;"

"...Happy is the generation where the elders listen to the juniors, and Kal v'Chomer vice-versa."

Question: It isn't a Kal v'Chomer - it's an obligation!?

Answer: It means, since the elders listen to the juniors, the juniors will make a Kal v'Chomer for themselves.

If Beis Din and all Israel saw the moon (on the 30th), witnesses were examined, and they didn't manage to say Mekudash before dark, it is a full month.

If Beis Din alone saw it, two of them should testify before the others.

If Beis Din alone saw it and there are only three of them, then two testify and the other is joined by other Dayanim.

This is because the single Dayan cannot sanctify it on his own.

Question: Why state that all Israel saw it (seeing as Beis Din anyway saw it)?

Answer: One might think that since all Israel saw it, it is public knowledge and shouldn't be made a full month.

Question: Since they all saw it, why does the Mishnah need to state that witnesses were examined?

Answer: It means "or" witnesses were examined.

Question: Since when everyone saw it, it didn't help, obviously it won't help if witnesses were examined either?

Answer: One might think that the sanctification is a conclusion of a single process that began with the witness examination by day, and is therefore valid even if done after dark;

This would be similar to monetary judgments that can finish at night if begun by day.

Question: Why is this not indeed true?

Answer: The Pasuk calls the sanctification of the moon a Chok, which refers to the end of the process, and calls it a Mishpat, which must be done by day.

Question: What is the point of two Dayanim testifying before the others - why should hearing it be any better than seeing it?

Answer: If it was seen at night, then seeing it is not adequate for sanctifying it.

Question: What is the point of two Dayanim (in the third case) testifying before the other one - why should hearing it be any better than seeing it?

Attempted answer: It is referring to where they saw it at night.

Objection: It is the same Chidush as the earlier case!

Answer: The Chidush is in the latter part, that one Dayan alone may not sanctify it.

One might think that it should be like monetary matters, which require three judges unless one is an expert.

Question: Why is it not like that?

Answer: There was no-one more expert than Moshe, and Hash-m said that Aharon was needed also.

We see here that a potential witness can act as a Dayan instead.

Question: The Mishnah therefore seems not to follow R. Akiva:

(R. Tarfon): If the Sanhedrin saw a murder, some can act as witnesses and the others as Dayanim.

(R. Akiva): They must all act as witnesses and none can act as Dayanim.

Answer: R. Akiva only held that view in cases of murder, where the Torah wants the Dayanim to find him innocent, which they won't do if they saw him do it.